(112e) Computation of Entropic Effects in Crystal Structures

Many compounds can form more than one crystal form, a phenomenon known as polymorphism.Although different polymorphs have the same chemical properties, their physical properties (e.g. solubility) differ significantly as a result of the different spatial arrangement of the molecules [1].

Over the last two decades, there has been significant progress in the development of computational methods for the prediction of the polymorphic forms in which a compound can crystallise. These predictions are mainly based on the lattice energy minimisation of a large number of trial structures [2,3,4,5]. Among the limitations of current methods, however, are that (i) the effect of entropy is ignored during the search, and (ii) a large number of candidate structures are generated.

In this study, a methodology is developed to calculate the entropic contribution to the free energy based on quasi-harmonic lattice dynamics [6]. This method is computationally cheap compared to other methods that can be used to evaluate the free energy of crystals. An approach based on Gauss-Legendre quadrature is proposed to evaluate the required integrals in the first Brillouin zone. It is shown to be significantly more efficient than the sampling methods used traditionally. Moreover, by removing the need for random sampling, a continuously differentiable function is obtained, making this approach suitable for gradient-based optimisation. Harmonic (dispersion curves, phonon density of states) and anharmonic properties (thermal expansivity) are calculated. The accuracy of the harmonic lattice dynamics method is tested by comparison against available experimental or calculated data.

References

 [1]  Bernstein, J., “Polymorphism in Molecular Crystals”. Clarendon Press, Oxford, (2002)

 [2]   P.G. Karamertzanis and C.C. Pantelides, J. Comput. Chem., 26, 304-324 (2005)

 [3]   P.G. Karamertzanis and C.C. Pantelides,  Molecular Physics,105(2-3),  273-291 (2007)

 [4]   A.V. Kazantsev et.al., J. Chem. Theory Comput., 7(6),  1998-2016 (2011)

 [5]   A.V. Kazantsev et.al., “CrystalOptimizer: An efficient algorithm for lattice energy minimisation of organic crystals using quantum mechanical calculations”, Molecular Systems Engineering, C.S. Adjiman and A. Galindo, Wiley-VCH

 [6]   M.T. Dove, “Introduction to lattice dynamics”, Cambridge University Press, (1993)